It's a 2000 iuzuki Rodeo lost Keys need codes for replacement Keys

Is it setting any fault code in the Powertrain computer?

not without breaking it and causing more problems ---if no spare key need to go to dealer with your vin number and proof of ownership and they can cut you new key(s)

Many keys today have a microchip in the key itself, and if the chip has malfunctioned the car won't respond normally. Your second key working is proof the trouble is in the key not the car. I think they can be checked in some Autoparts stores.

Are you saying it won't crank or won't start ?
If you need the procedure to check the timing marks on the cam gears that should be in a repair book or shop manual.
It is an interference engine, so you have to be careful and not crank the engine with the starter if the cams are not in time with the crank.

here is the procedure.

let me know if there is any thing else i can do for you.

the ignition switch AND the keys need to be coded by a dealer THIS IS NOT A DIY FIX.

replace the whole ignition barrel with new key and get key programmed by dealer
can remove barrel and key by removing steering column covers turn ignition to on position and with small shank screw driver push in hole in outer top rear section of barrel assembly then pull out ignition lock barrel with key in it. fit new lock barrel and key, program new key into system and can get door lock barrels coded to suit new key or get code for old key and cut new key so it fits mechanical locks on the rest of the vehicle (just wont turn in ignition) 2 keys for vehicle.

you will have to get a dealer to cut new keys to code that dealers have access to and then get them to program to car but also erase old keys so vehicle wont start with old keys
or next more expensive option is new keys, ignition barrel and door barrels replaced which are differently same coded key and locks as well as programming and erasing old keys.

try shaking the steering wheel back and forth when you turn the ignition off. also the vehicle must be in park to get the keys out

Try going to the junk yard its gonna get expensive